Equilibrium concentration changes

Transient, or time-resolved, techniques measure tire response of a substance after a rapid perturbation. A swift kick can be provided by any means tliat suddenly moves tire system away from equilibrium—a change in reactant concentration, for instance, or tire photodissociation of a chemical bond. Kinetic properties such as rate constants and amplitudes of chemical reactions or transfonnations of physical state taking place in a material are tlien detennined by measuring tire time course of relaxation to some, possibly new, equilibrium state. Detennining how tire kinetic rate constants vary witli temperature can further yield infonnation about tire tliennodynamic properties (activation entlialpies and entropies) of transition states, tire exceedingly ephemeral species tliat he between reactants, intennediates and products in a chemical reaction. 

If the equilibrium concentrations for A, B and C are a, b and c, respectively, the concentration changes resulting from the application of the perturbation will be... 

Letting x equal the change in the concentration of Pb +, the equilibrium concentrations are... 

Hundreds of metabohc reac tions take place simultaneously in cells. There are branched and parallel pathways, and a single biochemical may participate in sever distinct reactions. Through mass action, concentration changes caused by one reac tion may effect the kinetics and equilibrium concentrations of another. In order to prevent accumulation of too much of a biochemical, the product or an intermediate in the pathway may slow the production of an enzyme or may inhibit the ac tivation of enzymes regulating the pathway. This is termed feedback control and is shown in Fig. 24-1. More complicated examples are known where two biochemicals ac t in concert to inhibit an enzyme. As accumulation of excessive amounts of a certain biochemical may be the key to economic success, creating mutant cultures with defective metabolic controls has great value to the produc tion of a given produc t. 

Except as an index of respiration, carbon dioxide is seldom considered in fermentations but plays important roles. Its participation in carbonate equilibria affects pH removal of carbon dioxide by photosynthesis can force the pH above 10 in dense, well-illuminated algal cultures. Several biochemical reactions involve carbon dioxide, so their kinetics and equilibrium concentrations are dependent on gas concentrations, and metabolic rates of associated reactions may also change. Attempts to increase oxygen transfer rates by elevating pressure to get more driving force sometimes encounter poor process performance that might oe attributed to excessive dissolved carbon dioxide. 

Now, as equilibrium is maintained in the plate (p) by definition, the mass (dm) will bfe distributed between the two phases, resulting in a solute concentration change of dXm(p) in the mobile phase and dXs(p) in the stationary phase. Then,... 

Suppose the relaxation time t is determined under conditions such that reactant B is buffered that is, essentially no change in the concentration of B occurs during relaxation. Derive an expression for t in terms of the rate constants and equilibrium concentrations. 

Kgp values can be used to make predictions as to whether or not a precipitate will form when two solutions are mixed. To do this, we follow an approach very similar to that used in Chapter 12, to determine the direction in which a system will move to reach equilibrium. We work with a quantity Q, which has the same mathematical form as K. The difference is that the concentrations that appear in Q are those that apply at a particular moment. Those that appear in are equilibrium concentrations. Putting it another way, the value of Q is expected to change as a precipitation reaction proceeds, approaching Ksp and eventually becoming equal to it. 

We have already considered an example of the change of equilibrium concentrations as the temperature is altered. The relative amounts of N02 and N204 are readily and obviously affected by a temperature change. The equilibrium concentrations are affected if the temperature is altered. 

Catalysts increase the rate of reactions. It is found experimentally that addition of a catalyst to a system at equilibrium does not alter the equilibrium state. Hence it must be true that any catalyst has the same effect on the rates of the forward and reverse reactions. You will recall that the effect of a catalyst on reaction rates can be discussed in terms of lowering the activation energy. This lowering is effective in increasing the rate in both directions, forward and reverse. Thus, a catalyst produces no net change in the equilibrium concentrations even though the system may reach equilibrium much more rapidly than it did without the catalyst. 

We are not satisfied with the conclusion that this change or that change affects the equilibrium concentrations. We would also like to predict the direction of the effect (does it favor products or reactants ) and the magnitude of the effect (how much does it favor products or reactants ). The first desire, to know the qualitative effects, is answered by a generalization first proposed by a French chemist, Henry Louis Le Chatelier, and now called Le Chatelier s Principle. 

Does Le Chatelier s Principle predict a change of equilibrium concentrations for the following reactions if the gas mixture is compressed If so, does the change favor reactants or products ... 

What effect would the following changes have on the equilibrium concentration of Cl2 Give your reasons for each answer. 

Each of the following systems has come to equilibrium. What would be the effect on the equilibrium concentration (increase, decrease, no change) of each substance in the system when the listed reagent is added ... 

In thermodynamic equilibrium, the free energy has a minimum. Accordingly, F does not change with the number of introduced vacancies n. Feeding Eq. (2) into Eq. (3) results in the following equilibrium concentration of vacancies ... 

The equilibrium concentrations of many disubstituted benzenes (containing alkyl and halogen substituents) show that the meta isomer is in nearly all cases the most thermodynamically stable. It is not obvious why this should be so. Shine182 had discussed this problem in terms of the relative sizes of the standard enthalpy and entropy changes between any pair of isomers. 

Perturbation or chemical relaxation techniques cause an equilibrium to be upset by a sudden change in an external variable such as temperature, pressure, or electric field strength. One then measures the readjustment of the equilibrium concentrations. The time resolution may be as short as 10 10 s, although 10 6 s is the limit more commonly attainable. The method requires no mixing, which is why its time resolution is so good. On the other hand, it is applicable only to equilibria that are properly poised under the conditions used. 

Step 3 In the third row write the equilibrium concentrations by adding the change in concentration (step 2) to the initial concentration for each substance (step 1). 

Step 1 Initial concentration Step 2 Change in concentration Step 3 Equilibrium concentration... 

Example 4.2 used the method of false transients to solve a steady-state reactor design problem. The method can also be used to find the equilibrium concentrations resulting from a set of batch chemical reactions. To do this, formulate the ODEs for a batch reactor and integrate until the concentrations stop changing. This is illustrated in Problem 4.6(b). Section 11.1.1 shows how the method of false transients can be used to determine physical or chemical equilibria in multiphase systems. 

In Study 8. Ic we examined how the reactant concentrations affected the forward reaction rate, but we have not yet examined how such a change influences the equilibrium condition. Change the initial concentrations to [A]o = 700 cells... 

A typical simulation result is shown in Fig. 3. Under the given conditions, the concentration of fuel gas in bulk phase at the exit (Fig. 3a) is zero and the concentration of evaporative fuel gas at solid phase (Fig. 3b) at the exit did not reach the equilibrium concentration of activated carbon during adsorption. These results indicate that the canister of ORVR system is properly designed to adsorb the evaporative fuel gas. The temperature changes in canister (Fig. 3 c) during the operation remains in the acceptable range. The test results for different weather conditions showed that the canister design in this study can fulfill the required performance. 

Vapor pressure provides a simple illustration of why adding a pure liquid or solid does not change equilibrium concentrations. Recall from Chapter H that any liquid establishes a dynamic equilibrium with its vapor, and the partial pressure of the vapor at equilibrium is the vapor pressure. The vapor pressure is independent of the amount of liquid present. Figure 16-8 illustrates that the vapor pressure of water above a small puddle is the same as the vapor pressure above a large pond at the same temperature. More molecules escape from the larger surface of the pond, but more molecules are captured, too. The balance between captures and escapes is the same for both puddle and pond. 

A chemical system reacts, often rapidly, from initial conditions to equilibrium. As this occurs, concentrations of starting materials decrease, and concentrations of products increase. These concentration changes are related in two ways, as described in Section 4-. To review, the concentration of each reagent at equilibrium is its initial concentration plus the change that has occurred ... 

These relationships provide complete stoichiometric information regarding the equilibrium. Just as amounts tables are usetiil in doing stoichiometric calculations, a concentration table that provides initial concentrations, changes in concentrations, and equilibrium concentrations is an excellent way to organize Step 5 of the problem-solving... 

Construct a table of initial concentrations, changes in concentration, and equilibrium concentrations for each species that appears in the equilibrium constant expression. The equilibrium concentrations from the last row of the table are needed to find Kgq. Start by entering the data given in the problem. The initial concentration of benzoic acid is 0.125 M. Pure water contains no benzoate ions and a negligible concentration of hydronium ions. The problem also states the equilibrium concentration of hydronium ions, 0.0028 M. 

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